# std::normal_distribution

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< cpp‎ | numeric‎ | random

Defined in header `<random>` |  |
template< class RealType = double > class normal_distribution; |  | (since C++11)

Generates random numbers according to the Normal (or Gaussian) random number distribution. It is defined as:

  \(\small{f(x;\mu,\sigma)}=\frac{1}{\sigma\sqrt{2\pi} }\exp{(-\frac{1}{2}{(\frac{x-\mu}{\sigma})}^2)}\)f(x; μ,σ) =

  1
  σ√2π

  exp⎛
  ⎜
  ⎝

  -1
  2

  ⎛
  ⎜
  ⎝

  x-μ
  σ

  ⎞
  ⎟
  ⎠2
  ⎞
  ⎟
  ⎠

Here \(\small\mu\)μ is the Mean and \(\small\sigma\)σ is the Standard deviation (stddev).

`std::normal_distribution` satisfies all requirements of RandomNumberDistribution.

### Template parameters

RealType | - | The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

### Member types

Member type | Definition
`result_type` (C++11) | RealType
`param_type` (C++11) | the type of the parameter set, see RandomNumberDistribution.

### Member functions

(constructor) (C++11) | constructs new distribution (public member function)
reset (C++11) | resets the internal state of the distribution (public member function)
##### Generation
operator() (C++11) | generates the next random number in the distribution (public member function)
##### Characteristics
meanstddev (C++11) | returns the distribution parameters (public member function)
param (C++11) | gets or sets the distribution parameter object (public member function)
min (C++11) | returns the minimum potentially generated value (public member function)
max (C++11) | returns the maximum potentially generated value (public member function)

### Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20) | compares two distribution objects (function)
operator<<operator>> (C++11) | performs stream input and output on pseudo-random number distribution (function template)

### Example

Run this code

    #include <cmath>
    #include <iomanip>
    #include <iostream>
    #include <map>
    #include <random>
    #include <string>

    int main()
    {
        std::random_device rd{};
        std::mt19937 gen{rd()};

        // Values near the mean are the most likely. Standard deviation
        // affects the dispersion of generated values from the mean.
        std::normal_distribution d{5.0, 2.0};

        // Draw a sample from the normal distribution and round it to an integer.
        auto random_int = [&d, &gen]{ return std::lround(d(gen)); };

        std::map<long, unsigned> histogram{};
        for (auto n{10000}; n; --n)
            ++histogram[random_int()];

        for (const auto [k, v] : histogram)
            std::cout << std::setw(2) << k << ' ' << std::string(v / 200, '*') << '\n';
    }

Possible output:

    -1
     0
     1 *
     2 ***
     3 *****
     4 ********
     5 *********
     6 *********
     7 ******
     8 ***
     9 *
    10
    11

### External links

1. | Weisstein, Eric W. "Normal Distribution." From MathWorld — A Wolfram Web Resource.
2. | Normal distribution — From Wikipedia.

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